In this paper,we are concerned with a three-dimensional non-isothermal model for the compressible nematic liquid crystal flows in a periodic domain.Under some smallness and structural assumptions imposed on the time-p...In this paper,we are concerned with a three-dimensional non-isothermal model for the compressible nematic liquid crystal flows in a periodic domain.Under some smallness and structural assumptions imposed on the time-periodic force,we establish the existence of the time-periodic solutions to the system by using a regularized approximation scheme and the topological degree theory.We also prove a uniqueness result via energy estimates.展开更多
In a magnetohydrodynamic(MHD)driven fluid cell,a plane non-parallel flow in a square domain satisfying a free-slip boundary condition is examined.The energy dissipation of the flow is controlled by the viscosity and l...In a magnetohydrodynamic(MHD)driven fluid cell,a plane non-parallel flow in a square domain satisfying a free-slip boundary condition is examined.The energy dissipation of the flow is controlled by the viscosity and linear friction.The latter arises from the influence of the Hartmann bottom boundary layer in a three-dimensional(3D)MHD experiment in a square bottomed cell.The basic flow in this fluid system is a square eddy flow exhibiting a network of N~2 vortices rotating alternately in clockwise and anticlockwise directions.When N is odd,the instability of the flow gives rise to secondary steady-state flows and secondary time-periodic flows,exhibiting similar characteristics to those observed when N=3.For this reason,this study focuses on the instability of the square eddy flow of nine vortices.It is shown that there exist eight bi-critical values corresponding to the existence of eight neutral eigenfunction spaces.Especially,there exist non-real neutral eigenfunctions,which produce secondary time-periodic flows exhibiting vortices merging in an oscillatory manner.This Hopf bifurcation phenomenon has not been observed in earlier investigations.展开更多
We show existence of time-periodic supersonic solutions in a finite interval, after certain start-up time depending on the length of the interval, to the one space-dimensional isentropic compressible Euler equations, ...We show existence of time-periodic supersonic solutions in a finite interval, after certain start-up time depending on the length of the interval, to the one space-dimensional isentropic compressible Euler equations, subjected to periodic boundary conditions. Both classical solutions and weak entropy solutions, as well as high-frequency limiting behavior are considered. The proofs depend on the theory of Cauchy problems of genuinely nonlinear hyperbolic systems of conservation laws.展开更多
In this note it is shown that the Vlasov-Poisson-Fokker-Planck system in the three-dimensional whole space driven by a time-periodic background profile near a positive constant state admits a time-periodic small-ampli...In this note it is shown that the Vlasov-Poisson-Fokker-Planck system in the three-dimensional whole space driven by a time-periodic background profile near a positive constant state admits a time-periodic small-amplitude solution with the same period. The proof follows by the Serrin's method on the basis of the exponential time-decay property of the linearized system in the case of the constant background profile.展开更多
In this work,the effects of externally applied axial pressure gradients and transverse magnetic fields on the electrokinetic energy conversion(EKEC)efficiency and the streaming potential of nanofluids through a microa...In this work,the effects of externally applied axial pressure gradients and transverse magnetic fields on the electrokinetic energy conversion(EKEC)efficiency and the streaming potential of nanofluids through a microannulus are studied.The analytical solution for electro-magneto-hydro-dynamic(EMHD)flow is obtained under the condition of the Debye-Huuckel linearization.Especially,Green’s function method is used to obtain the analytical solutions of the velocity field.The result shows that the velocity distribution is characterized by the dimensionless frequency?,the Hartmann number Ha,the volume fraction of the nanoparticlesφ,the geometric radius ratio a,and the wallζpotential ratio b.Moreover,the effects of three kinds of periodic excitations are compared and discussed.The results also show that the periodic excitation of the square waveform is more effective in increasing the streaming potential and the EKEC efficiency.It is worth noting that adjusting the wallζpotential ratio and the geometric radius ratio can affect the streaming potential and the EKEC efficiency.展开更多
The compressible Navier-Stokes equations driven by a time-periodic external force are considered in this article. We establish the existence of weak time-periodic solutions and improve the result from [3] in the follo...The compressible Navier-Stokes equations driven by a time-periodic external force are considered in this article. We establish the existence of weak time-periodic solutions and improve the result from [3] in the following sense: we extend the class of pressure functions, that is, we consider lower exponent γ.展开更多
In this paper, we investigate the existence of time-periodic solutions to the n-dimension hydrodynamic model for a reacting mixture with a time-periodic external force when the dimension is under some smallness assump...In this paper, we investigate the existence of time-periodic solutions to the n-dimension hydrodynamic model for a reacting mixture with a time-periodic external force when the dimension is under some smallness assumption. The energy method combined with the spectral analysis is used to obtain the optimal decay estimates on the linearized solution operator. We study the existence and uniqueness of the time-periodic solution in some suitable function space by using a fixed point method and the decay estimates. Furthermore, we obtain the time asymptotic stability of the time-periodic solution.展开更多
For quasilinear hyperbolic systems on general networks with time-periodic boundary-interface conditions with a dissipative structure,the existence and stability of the time-periodic classical solutions are discussed.
In this paper,we develop a new algorithm to find the exact solutions of the Einstein's field equations.Time-periodic solutions are constructed by using the new algorithm.The singularities of the time-periodic solu...In this paper,we develop a new algorithm to find the exact solutions of the Einstein's field equations.Time-periodic solutions are constructed by using the new algorithm.The singularities of the time-periodic solutions are investigated and some new physical phenomena,such as degenerate event horizon and time-periodic event horizon,are found.The applications of these solutions in modern cosmology and general relativity are expected.展开更多
In this paper,we construct several kinds of new time-periodic solutions of the vacuum Einstein's field equations whose Riemann curvature tensors vanish,keep finite or take the infinity at some points in these spac...In this paper,we construct several kinds of new time-periodic solutions of the vacuum Einstein's field equations whose Riemann curvature tensors vanish,keep finite or take the infinity at some points in these space-times,respectively.The singularities of these new time-periodic solutions are investigated and some new physical phenomena are discovered.展开更多
In this paper we consider the physical characters of the new time-periodic solution of the vacuum Einstein’s field equations which was constructed by Kong, Liu and Shen. By the analysis of the Penrose diagram associa...In this paper we consider the physical characters of the new time-periodic solution of the vacuum Einstein’s field equations which was constructed by Kong, Liu and Shen. By the analysis of the Penrose diagram associated with this solution, we find that this solution is very different from the other solutions.展开更多
This paper is concerned with the boundary-value problem on the Boltzmann equation in bounded domains with diffuse-reflection boundary where the boundary temperature is time-periodic. We establish the existence of time...This paper is concerned with the boundary-value problem on the Boltzmann equation in bounded domains with diffuse-reflection boundary where the boundary temperature is time-periodic. We establish the existence of time-periodic solutions with the same period for both hard and soft potentials, provided that the time-periodic boundary temperature is sufficiently close to a stationary one which has small variations around a positive constant. The dynamical stability of time-periodic profiles is also proved under small perturbations, and this in turn yields the non-negativity of the profile. For the proof, we develop new estimates in the time-periodic setting.展开更多
In this paper,we investigate the time-periodic solution to a coupled compressible Navier–Stokes/Allen–Cahn system which describes the motion of a mixture of two viscous compressible fluids with a time periodic exter...In this paper,we investigate the time-periodic solution to a coupled compressible Navier–Stokes/Allen–Cahn system which describes the motion of a mixture of two viscous compressible fluids with a time periodic external force in a periodic domain in R^N.The existence of the time-periodic solution to the system is established by using an approach of parabolic regularization and combining with the topology degree theory,and then the uniqueness of the period solution is obtained under some smallness and symmetry assumptions on the external force.展开更多
In this work, the authors considered the periodic optimal control problem of Fitzhugh-Nagumo equation. They firstly prove the existence of time-periodic solution to Fitzhugh-Nagumo equation. Then they show the existen...In this work, the authors considered the periodic optimal control problem of Fitzhugh-Nagumo equation. They firstly prove the existence of time-periodic solution to Fitzhugh-Nagumo equation. Then they show the existence of optimal solution to the optimal control problem, and finally the first order necessary condition is obtained by constructing an appropriate penalty function.展开更多
This paper presents an analytical solution for natural convection flow in a vertical annulus due to time-periodic heating of annulus surfaces.Closed-form expressions for velocity,temperature,skin-friction,mass flow ra...This paper presents an analytical solution for natural convection flow in a vertical annulus due to time-periodic heating of annulus surfaces.Closed-form expressions for velocity,temperature,skin-friction,mass flow rate and rate of heat transfer which is expressed as Nusselt number are obtained by solving the present mathematical model after separating into steady component and periodic regime.The effects of pertinent parameters such as Strouhal number(St),Prandtl number(Pr)and radius ratio(λ)are shown with the aid of contour and line graphs.Results indicate that the role of Strouhal number and Prandtl number is to decrease fluid velocity,temperature and skin-friction.Furthermore,increase in Strouhal number increases the temperature phase-lag.展开更多
This paper investigates the phenomenon of stochastic resonance in a single-mode laser driven by time-modulated correlated coloured noise sources. The power spectrum and signal-to-noise ratio R of the laser intensity a...This paper investigates the phenomenon of stochastic resonance in a single-mode laser driven by time-modulated correlated coloured noise sources. The power spectrum and signal-to-noise ratio R of the laser intensity are calculated by the linear approximation. The effects caused by noise self-correlation time τ1, τ2 and cross-correlated time τ3 for stochastic resonance are analysed in two ways: τ1, τ2 and τ3 are taken to be the independent variables and the parameters respectively. The effects of the gain coefficient F and loss coefficient K on the stochastic resonance are also discussed. It is found that besides the presence of the standard form and the broad sense of stochastic resonance, the number of extrema in the curve of R versus K is reduced with the increase of the gain coefficient Г.展开更多
基金partially supported by the Science and Technology Research Program of Chongqing Municipal Education Commission(KJQN202100523,KJQN202000536)the National Natural Science Foundation of China(12001074)+3 种基金the Natural Science Foundation of Chongqing(cstc2020jcyj-msxmX0606)supported by the National Natural Science Foundation of Chongqing(CSTB2023NSCQ-MSX0278)the Science and Technology Research Program of Chongqing Municipal Education Commission(KJZD-K202100503)the Research Project of Chongqing Education Commission(CXQT21014)。
文摘In this paper,we are concerned with a three-dimensional non-isothermal model for the compressible nematic liquid crystal flows in a periodic domain.Under some smallness and structural assumptions imposed on the time-periodic force,we establish the existence of the time-periodic solutions to the system by using a regularized approximation scheme and the topological degree theory.We also prove a uniqueness result via energy estimates.
基金Project supported by the National Natural Science Foundation of China(No.11571240)the Shenzhen Natural Science Fund of China(the Stable Support Plan Program No.20220805175116001)。
文摘In a magnetohydrodynamic(MHD)driven fluid cell,a plane non-parallel flow in a square domain satisfying a free-slip boundary condition is examined.The energy dissipation of the flow is controlled by the viscosity and linear friction.The latter arises from the influence of the Hartmann bottom boundary layer in a three-dimensional(3D)MHD experiment in a square bottomed cell.The basic flow in this fluid system is a square eddy flow exhibiting a network of N~2 vortices rotating alternately in clockwise and anticlockwise directions.When N is odd,the instability of the flow gives rise to secondary steady-state flows and secondary time-periodic flows,exhibiting similar characteristics to those observed when N=3.For this reason,this study focuses on the instability of the square eddy flow of nine vortices.It is shown that there exist eight bi-critical values corresponding to the existence of eight neutral eigenfunction spaces.Especially,there exist non-real neutral eigenfunctions,which produce secondary time-periodic flows exhibiting vortices merging in an oscillatory manner.This Hopf bifurcation phenomenon has not been observed in earlier investigations.
基金supported by the National Natural Science Foundation of China(11371141 and 11871218)Science and Technology Commission of Shanghai Municipality(STCSM)under Grant No.18dz2271000
文摘We show existence of time-periodic supersonic solutions in a finite interval, after certain start-up time depending on the length of the interval, to the one space-dimensional isentropic compressible Euler equations, subjected to periodic boundary conditions. Both classical solutions and weak entropy solutions, as well as high-frequency limiting behavior are considered. The proofs depend on the theory of Cauchy problems of genuinely nonlinear hyperbolic systems of conservation laws.
基金supported by the General Research Fund(Project No.409913)from RGC of Hong Kongsupported by grants from the National Natural Science Foundation of China(11101188 and 11271160)
文摘In this note it is shown that the Vlasov-Poisson-Fokker-Planck system in the three-dimensional whole space driven by a time-periodic background profile near a positive constant state admits a time-periodic small-amplitude solution with the same period. The proof follows by the Serrin's method on the basis of the exponential time-decay property of the linearized system in the case of the constant background profile.
基金Project supported by the National Natural Science Foundation of China(Nos.11772162,11802147)the Natural Science Foundation of Inner Mongolia(No.2018LH01015)+1 种基金the Foundation of Inner Mongolia Autonomous Region University Scientific Research Project(No.NJZY18093)the Foundation of Inner Mongolia University of Technology(No.ZD201714)。
文摘In this work,the effects of externally applied axial pressure gradients and transverse magnetic fields on the electrokinetic energy conversion(EKEC)efficiency and the streaming potential of nanofluids through a microannulus are studied.The analytical solution for electro-magneto-hydro-dynamic(EMHD)flow is obtained under the condition of the Debye-Huuckel linearization.Especially,Green’s function method is used to obtain the analytical solutions of the velocity field.The result shows that the velocity distribution is characterized by the dimensionless frequency?,the Hartmann number Ha,the volume fraction of the nanoparticlesφ,the geometric radius ratio a,and the wallζpotential ratio b.Moreover,the effects of three kinds of periodic excitations are compared and discussed.The results also show that the periodic excitation of the square waveform is more effective in increasing the streaming potential and the EKEC efficiency.It is worth noting that adjusting the wallζpotential ratio and the geometric radius ratio can affect the streaming potential and the EKEC efficiency.
基金supported by National Natural Science Foundation of China-NSAF(11271305,11531010)the Fundamental Research Funds for Xiamen University(201412G004)supported by National Natural Science Foundation of ChinaNSAF(11271305,11531010)
文摘The compressible Navier-Stokes equations driven by a time-periodic external force are considered in this article. We establish the existence of weak time-periodic solutions and improve the result from [3] in the following sense: we extend the class of pressure functions, that is, we consider lower exponent γ.
文摘In this paper, we investigate the existence of time-periodic solutions to the n-dimension hydrodynamic model for a reacting mixture with a time-periodic external force when the dimension is under some smallness assumption. The energy method combined with the spectral analysis is used to obtain the optimal decay estimates on the linearized solution operator. We study the existence and uniqueness of the time-periodic solution in some suitable function space by using a fixed point method and the decay estimates. Furthermore, we obtain the time asymptotic stability of the time-periodic solution.
基金supported by the National Natural Science Foundation of China(Nos.12122104,11831011)Shanghai Science and Technology Programs(Nos.21ZR1406000,21JC1400600,19JC1420101)。
文摘For quasilinear hyperbolic systems on general networks with time-periodic boundary-interface conditions with a dissipative structure,the existence and stability of the time-periodic classical solutions are discussed.
基金supported by National Natural Science Foundation of China (Grant Nos.10671124)
文摘In this paper,we develop a new algorithm to find the exact solutions of the Einstein's field equations.Time-periodic solutions are constructed by using the new algorithm.The singularities of the time-periodic solutions are investigated and some new physical phenomena,such as degenerate event horizon and time-periodic event horizon,are found.The applications of these solutions in modern cosmology and general relativity are expected.
基金supported in part by National Natural Science Foundation of China (Grant No.10971190)the Qiu-Shi Professor Fellowship from Zhejiang University,China
文摘In this paper,we construct several kinds of new time-periodic solutions of the vacuum Einstein's field equations whose Riemann curvature tensors vanish,keep finite or take the infinity at some points in these space-times,respectively.The singularities of these new time-periodic solutions are investigated and some new physical phenomena are discovered.
文摘In this paper we consider the physical characters of the new time-periodic solution of the vacuum Einstein’s field equations which was constructed by Kong, Liu and Shen. By the analysis of the Penrose diagram associated with this solution, we find that this solution is very different from the other solutions.
基金Supported by the National Natural Science Foundation of China (No. 10671182) the Excellent Youth Teachers Foundation of High College of Henan Province.
基金partially supported by the General Research Fund(Project No.14302817)from RGC of Hong Konga Direct Grant(No.4053286)from CUHKpartly supported by NSFC Grant No.11771429,11688101,and 11671237
文摘This paper is concerned with the boundary-value problem on the Boltzmann equation in bounded domains with diffuse-reflection boundary where the boundary temperature is time-periodic. We establish the existence of time-periodic solutions with the same period for both hard and soft potentials, provided that the time-periodic boundary temperature is sufficiently close to a stationary one which has small variations around a positive constant. The dynamical stability of time-periodic profiles is also proved under small perturbations, and this in turn yields the non-negativity of the profile. For the proof, we develop new estimates in the time-periodic setting.
基金Supported by the NNSF of China(Grant Nos.11671367 and 11801133)the Natural Science Foundation of Henan Province(Grant No.152300410227)the Key Research Projects of Henan Higher Education Institutions(Grant No.18A110038)。
文摘In this paper,we investigate the time-periodic solution to a coupled compressible Navier–Stokes/Allen–Cahn system which describes the motion of a mixture of two viscous compressible fluids with a time periodic external force in a periodic domain in R^N.The existence of the time-periodic solution to the system is established by using an approach of parabolic regularization and combining with the topology degree theory,and then the uniqueness of the period solution is obtained under some smallness and symmetry assumptions on the external force.
基金supported by the Fundamental Research Funds for the Central Universities,ChinaUniversity of Geosciences(Wuhan)(CUGSX01).
文摘In this work, the authors considered the periodic optimal control problem of Fitzhugh-Nagumo equation. They firstly prove the existence of time-periodic solution to Fitzhugh-Nagumo equation. Then they show the existence of optimal solution to the optimal control problem, and finally the first order necessary condition is obtained by constructing an appropriate penalty function.
文摘This paper presents an analytical solution for natural convection flow in a vertical annulus due to time-periodic heating of annulus surfaces.Closed-form expressions for velocity,temperature,skin-friction,mass flow rate and rate of heat transfer which is expressed as Nusselt number are obtained by solving the present mathematical model after separating into steady component and periodic regime.The effects of pertinent parameters such as Strouhal number(St),Prandtl number(Pr)and radius ratio(λ)are shown with the aid of contour and line graphs.Results indicate that the role of Strouhal number and Prandtl number is to decrease fluid velocity,temperature and skin-friction.Furthermore,increase in Strouhal number increases the temperature phase-lag.
文摘This paper investigates the phenomenon of stochastic resonance in a single-mode laser driven by time-modulated correlated coloured noise sources. The power spectrum and signal-to-noise ratio R of the laser intensity are calculated by the linear approximation. The effects caused by noise self-correlation time τ1, τ2 and cross-correlated time τ3 for stochastic resonance are analysed in two ways: τ1, τ2 and τ3 are taken to be the independent variables and the parameters respectively. The effects of the gain coefficient F and loss coefficient K on the stochastic resonance are also discussed. It is found that besides the presence of the standard form and the broad sense of stochastic resonance, the number of extrema in the curve of R versus K is reduced with the increase of the gain coefficient Г.